机械振动辅助电导率成像的数学建模
Mathematical modeling of mechanical vibration assisted conductivity imaging
摘要：
本文的目的是数学建模的一个新的多物理场电导率成像系统，将机械振动同时施加到一个成像对象与电流注入。我们通过在边界上施加时谐机械振动来扰动内部电导率分布。这增强了任何电导率不连续性对感应内部电流密度分布的影响。与其他电导率对比度增强框架不同，它不需要参考数据的先验知识。在本文中，我们提供了一个数学框架，这种新的成像方式。作为振动辅助阻抗成像框架的一个应用，我们提出了一种新的电阻抗断层成像（EIT）中的乳房图像重建方法。作为它的另一个应用，我们研究了电导率异常检测问题，并提供了一个有效的位置搜索算法。我们分析和数值计算表明，所施加的机械振动增加了数据的电导率对比度的灵敏度，并提高了重建图像和异常检测结果的质量。对于阻抗成像中的许多应用，所提出的多物理场方法开辟了一个新的差分成像领域，称为振动差分成像，其可以增强时间差和频率差成像方法以提高灵敏度。
英文摘要：
This paper aims at mathematically modeling a new multi-physics conductivity imaging system incorporating mechanical vibrations simultaneously applied to an imaging object together with current injections. We perturb the internal conductivity distribution by applying time-harmonic mechanical vibrations on the boundary. This enhances the effects of any conductivity discontinuity on the induced internal current density distribution. Unlike other conductivity contrast enhancing frameworks, it does not require a prior knowledge of a reference data. In this paper, we provide a mathematical framework for this novel imaging modality. As an application of the vibration-assisted impedance imaging framework, we propose a new breast image reconstruction method in electrical impedance tomography (EIT). As its another application, we investigate a conductivity anomaly detection problem and provide an efficient location search algorithm. We show both analytically and numerically that the applied mechanical vibration increases the data sensitivity to the conductivity contrast and enhances the quality of reconstructed images and anomaly detection results. For numerous applications in impedance imaging, the proposed multi-physics method opens a new difference imaging area called the vibration-difference imaging, which can augment the time-difference and also frequency-difference imaging methods for sensitivity improvements.
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